Dozens of sharia courts in the UK are regularly giving illegal advice on issues including marriage and divorce, a report published today claims.

Decisions concerning marriages not recognised under English law, polygamy, and disputes regarding children are being made by at least 85 sharia courts, according to the report by the thinktank Civitas.

There is no clear divide between the functions of imams and the sharia courts. An imam who conducts a marriage which is not registered and then advises on disputes within that marriage acts in breach of the law and outside the scope of the sharia court's role, Civitas say.

"Some of these courts are advising illegal actions," said Denis MacEoin, a former lecturer in Arabic and Islamic studies who wrote the report. "And others transgress human rights standards."

Muslim arbitration tribunal (MTA), a network of sharia courts, has been operating in London, Manchester, Bradford, Birmingham and Nuneaton since 2007 under the 1996 Arbitration Act. These make decisions that are legally binding and can be enforced by the English courts, provided they do not conflict with English law and both parties choose to use them.

An MTA spokeswoman said that critics of any use of Islamic law failed to recognise that both parties had to agree to any form of dispute resolution in Britain.

"The establishment of Muslim Arbitration Tribunals is an important and significant step towards providing the Muslim community with a real opportunity to self determine disputes in accordance with Islamic sacred law," a statement from the organisation said.

But today's report claims that many smaller and often informal courts are making decisions under sharia law beyond their legal remit.

"About two-thirds of Muslim marriages are not being registered under the Marriages Act, which is illegal," said Neil Addison, a barrister specialising in the law on religion. "A woman with such a marriage would have no choice but to go to a sharia tribunal … But it's not the way arbitration is supposed to work."

MacEoin said: "By demanding marriage under Muslim law, the divorce is determined by the man saying 'I divorce you' three times. Divorce under Islamic law also affects the wife's entitlement to alimony, custody of children, and who keeps the family house. These will all be decided by sharia law and will be discriminatory towards the woman in all cases."

A decision last year by the UK's highest court caused controversy when it said sharia law was "wholly incompatible" with human rights law.

The House of Lords, granting asylum to a woman whose child would have been removed and placed with an abusive father under sharia law in Lebanon, described sharia in the country as "created by and for men in a male dominated society".

There has also been high-profile support for sharia courts however, from figures including the archbishop of Canterbury, Rowan Williams, who last year said that formal recognition of sharia law "seemed unavoidable".

Many Muslim lawyers have compared the operation of sharia courts to the Jewish beth din, which also operate as arbitration tribunals under UK law, a comparison which is questioned by the report.

The report disputes the comparison. "These courts are not operating within the same disciplines as the beth din", said Addison. "The beth din acknowledge that 'the law of the land is the law.' and a rabbi cannot perform a synagogue marriage ceremony unless a registrar is present to simultaneously register the marriage under English law."

"Imams and mosques are performing marriage ceremonies that are not registered under English law," Addison added. "They are the only religion that are doing it … Hindus and Sikhs have registered their temples under the Marriages Act."

The report's findings raise questions about the appropriate scope of tribunals under the Arbitration Act, experts say, which were not intended to deal with issues like divorce.

Sharia courts also need to be more transparent if they are to continue, critic says. "These tribunals don't seem to have any system of record keeping" said MacEion. "They are not transparent – either within their own community or for the outside community. That is a problem that needs to be looked at."